\documentclass{standalone}
\usepackage[active,tightpage]{preview}
\usepackage{amsmath}
\usepackage{pgfplots}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{arrows.meta,intersections}
\usepackage{pgffor}
\usepackage{ifthen}

\usepackage{anyfontsize}
\renewcommand{\normalsize}{\fontsize{12pt}{14pt}\selectfont}

\pgfplotsset{compat=1.18}
\PreviewEnvironment{tikzpicture}

\begin{document}

\begin{tikzpicture}

  \begin{axis}[
    axis lines=middle,
    xlabel={$x$},
    ylabel={$y$},
    xlabel style={xshift=10pt,yshift=-15pt},
    ylabel style={xshift=-15pt},
    xtick={0,...,6},
    ytick={0,...,6},
    grid=major,
    major grid style={gray!50}, 
    ymin=0,
    ymax=6.75,
    xmin=0,
    xmax=6.5,
    clip=false,
    axis on top=false,
    scale=2,
    axis equal image,
    axis line style={thick},
    width=8cm,
    legend style={at={(0.03,0.97)},anchor=north west},
  ] 
  
  \draw[thick,red] (axis cs: 1, 2) -- (axis cs: 1, 3);
  \draw[thick,blue] (axis cs: 1, 3) -- (axis cs: 2, 3);
  \draw[thick,red] (axis cs: 2, 3) -- (axis cs: 2, 4);
  \draw[thick,blue] (axis cs: 2, 4) -- (axis cs: 3, 4);
  \draw[thick,red] (axis cs: 3, 4) -- (axis cs: 3, 5);
  \draw[thick,red] (axis cs: 4, 4) -- (axis cs: 4, 5);
  \draw[thick,blue] (axis cs: 4, 5) -- (axis cs: 5, 5);
  \draw[thick,red] (axis cs: 5, 5) -- (axis cs: 5, 6);
  \draw[thick,red] (axis cs: 6, 5) -- (axis cs: 6, 6);

  \node [xshift=11pt,yshift=-4pt] at (axis cs: 0, 11/5) {$\color{blue}{UU}$};
  \node [xshift=5pt,yshift=-4pt] at (axis cs: 1, 14/5) {$\color{red}{R}$};
  \node [xshift=3pt,yshift=-6pt] at (axis cs: 4/3, 3) {$\color{blue}{U}$};
  \node [xshift=5pt,yshift=-4pt] at (axis cs: 2, 17/5) {$\color{red}{R}$};
  \node [xshift=9pt,yshift=-5pt] at (axis cs: 3, 4) {$\color{blue}{U}\color{red}{R}$};
  \node [xshift=5pt,yshift=-4pt] at (axis cs: 4, 23/5) {$\color{red}{R}$};
  \node [xshift=3pt,yshift=-6pt] at (axis cs: 14/3, 5) {$\color{blue}{U}$};
  \node [xshift=5pt,yshift=-4pt] at (axis cs: 5, 26/5) {$\color{red}{R}$};
  \node [xshift=5pt,yshift=-4pt] at (axis cs: 6, 29/5) {$\color{red}{R}$};

  \addplot [very thick,black,samples=100,domain=0:6] { (3 * x + 11) / 5 };
  \node [draw,fill=white,circle,inner sep=-1.5pt] at (axis cs: 0, 11/5) {};
  \node [draw,fill=black,circle,inner sep=-1.5pt] at (axis cs: 6, 29/5) {};

  \node[below left] at (axis cs: 0, 0) {$O$};

  \node[draw,fill=white] at (axis cs: 4, 2) {
    $\begin{aligned}&y=\dfrac{3x+11}{5},~x\in(0,6]\\&S=UURURURRURR\end{aligned}$
  };
  
  \end{axis}

\end{tikzpicture}

\end{document}